An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions

Journal Article · Mon Mar 14 00:00:00 EDT 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3555274· OSTI ID:21560047

Jian, Liu; Miller, William H ^[1]

---

1. Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460 (United States) and Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-1460 (United States)

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

• OSTI ID: 21560047
• Journal Information: Journal of Chemical Physics, Vol. 134, Issue 10; Other Information: DOI: 10.1063/1.3555274; (c) 2011 American Institute of Physics; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
BOLTZMANN-VLASOV EQUATION
CLEBSCH-GORDAN COEFFICIENTS
COMPLEXES
CORRELATION FUNCTIONS
DISTRIBUTION
EQUILIBRIUM
HARMONIC OSCILLATORS
IMPLEMENTATION
MATHEMATICAL OPERATORS
PHASE SPACE
POTENTIALS
QUANTUM MECHANICS
TEMPERATURE RANGE 0400-1000 K
TRAJECTORIES
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
TEMPERATURE RANGE